A Contribution to a
Book Symposium on John Leslie’s Modern Cosmology and Philosophy

Canadian Philosophical
Association and Canadian Society of Christian PhilosophersLaval University, 26
May 2001

WILLIAM L. VANDERBURGHWichita State University

It
can’t be doubted: we live in a universe in which life is possible.What
is in some doubt is just what to make of this fact.My
view of the matter is that very little can be made of this fact,
given the present state of cosmological knowledge.My
comments today will bear on the issue of whether or not there are fundamental
cosmological parameters that are “fine-tuned” for life; where we shall
take “fine-tuning” to mean simply that the parameters could have been different,
and if they had been ever so slightly different the universe would not
have been hospitable to life.

Cosmologists
generally take it that there is strong evidence for fine-tuning.Some
philosophers have tried to make Design Arguments from this evidence for
fine-tuning to the existence of a creative entity such as God; more specifically,
some have tried to argue that either fine-tuning implies a Designer, or
it implies the existence of multiple worlds.In
the latter case we explain the seeming specialness of fine-tuning by appeal
to the Anthropic Principle.I’m
not go to weigh in on this debate at all.I
happen to agree with Hume that Design arguments are fundamentally flawed,
but my point today is elsewhere.What
I want to do is to show that certain fundamental assumptions in modern
cosmology are very much less well established than is commonly taken
to be the case.In particular
I will argue for two points.First,
that in fact we have no evidence that General Relativity (GR)
applies to the universe as a whole, and second, that it might be impossible
to obtain any evidence that would make us confident in the applicability
of GR or any other theory of gravitation to the cosmos as a whole.

GR
is of course Einstein’s relativistic theory of space, time and gravitation.In
its gravitational aspect GR is a fundamental ingredient in almost every
idea in cosmology, from the origin, expansion and age of the universe,
to large scale structure, to galactic evolution and stellar fusion; in
other words, cosmology is shot through with GR.If
I’m right that the evidential warrant for GR in most of these contexts
is actually not very strong, and is perhaps not improvable, a great many
of the “facts” of cosmology are consequently quite a bit less well established
than is commonly taken to be the case.The
corollary of this that is of interest here is that much of the supposed
evidence for fine-tuning will turn out to be not very strong.If
this is so, we should put aside attempts even to say that the universe
appears to be fine-tuned, let alone attempts to make inferences from the
supposed fine-tuning to some philosophical conclusion about God or multiple
worlds.

Now,
my argument is just concerning GR, so only those fine-tuning arguments
that involve GR are directly cast into doubt by the reasoning I will present.There
might be other cases of fine-tuning (say, regarding the ratio of the nuclear
forces) that do not rely on GR, and upon which one could more reliably
construct Design or other types of arguments.I
will leave these cases aside, except to say two things.First,
note that if most of cosmology—that is, the very large proportion of it
that relies on GR—is of too low epistemic standing to license philosophical
arguments, whatever is left over will probably not be enough to mount a
convincing argument about Design or multiple worlds.It
seems to me we would need pervasive evidence of fine-tuning to even
get off the ground, and the remainders of fine-tuning left over after my
argument are probably insufficient for this purpose.Second,
the reasons for doubting the epistemic standing of GR as applied to the
cosmos also raise possible doubts about the other theories upon which the
remainder fine-tuning evidence relies.

My
own interests in modern cosmology have to do with evidence and methodology.I
think that cosmological theorizing and especially the creative ways in
which cosmologists bring evidence to bear on their theories, is of immense
philosophical interest—in particular as an example of empirical reasoning
under extremely evidence-poor and otherwise epistemically difficult conditions.Even
though my view is that this difficult epistemic position means that the
evidence for cosmological theories is really not very strong (compared,
say, to our evidence about celestial mechanics, or terrestrial geology),
I still agree with cosmologists who are eager to insist that modern cosmology
is a science.It is just that
it seems inevitable that our evidence for cosmological theories will never
be epistemically comparable to, say, our theories of biological evolution.This
is something that should inspire in us an appropriate caution when we are
tempted to draw philosophical conclusions from the current state of cosmology.

With
these preliminaries out of the way, let me turn now to the argument itself.What
got me thinking along these lines were some papers by G.F.R. Ellis, including
one anthologized by Leslie.Let
me turn now to discussing Ellis’s position on GR in the context of cosmological
spacetime structure.Afterwards
I will go on to consider the evidential status of GR in astrophysics and
cosmology.Here I’ll be drawing
on some of my own work on the dynamical dark matter problem to show that
we don’t have good reason to think that GR applies to galaxies or larger
dynamical structures, let alone to the universe as a whole.

General
Relativity predicts and explains, to a very high degree of precision, a
wide variety of phenomena.The
main phenomena in question are the motions of bodies in the solar system
(including Mercury’s excess perihelion precession), the gravitational redshift
of light, the Shapiro time delay for signals passing near the Sun, the
gravitational bending of light rays by massive bodies, and the formation
of black holes.GR has been
shown to account for all these phenomena better than every alternative
gravitational theory that has yet been constructed (see Will, 1993).GR’s
successes are nothing if not impressive, and surely they do confer a great
deal of epistemic warrant on the theory.As
it turns out, however, all these are tests on stellar system scales, and
they are really the only available tests for theories of gravitation.All
the epistemic warrant for GR, therefore, concerns its applicability to
stellar system scales.I’ll
use the phrase “stellar system scales” to refer to systems roughly similar
to our solar system in size; I want to include gravitational interactions
up to this scale, even though almost all of the tests just mentioned involve
interactions at much shorter scales, because GR also successfully accounts
for the decay of the orbits of binary pulsars through its prediction of
the emission of gravitational radiation.[1]

The
success of GR with regard to these tests is usually taken to provide warrant
for the applicability of GR to larger dynamical systems such as galaxies
and clusters of galaxies, and even to the evolution and structure of the
universe as a whole.But the
applicability of GR at larger scales can be no more than an assumption
in the present evidential context.(See
Mannheim 1994 and Ellis 1975, 1980, 1985, 1999.)As
with Newton’s argument to Universal Gravitation, we perform an inductive
generalization upon a set of “locally-derived” pieces of evidence, where
this evidence is consistent with itself and ideally involves independent
measures of theoretical parameters from several phenomena.Newton’s
extension of the principle of mutual gravitation to all bodies is
the step of the argument on which the inductive risk is focused (Smith
1999).As we know, Newton’s
bet here failed: extending Universal Gravity to all phenomena on the basis
of short-scale, weak-field tests, turned out to be incorrect.In
the same way, it is evidentially risky to extend GR to all dynamical systems
regardless of scale merely on the basis of stellar system or shorter scale
tests.This might not be cause
for worry except that there is evidence that suggests that GR might in
fact be inapplicable at galactic and greater scales—that is, that analogously
to the way Newtonian Universal Gravitation is the low-velocity, weak-field
limit of GR, GR could be the short-scale limit of some other yet-to-be-discovered
relativistic gravitation theory that applies at galactic and greater scales.

Let
me take the two relevant cases in turn, starting with the evidence for
GR’s applicability to the universe as a whole, and then the evidence for
GR’s applicability to large scale dynamical systems.Ellis
(1985) has argued persuasively that cosmology not only in fact relies
on unverified assumptions (for example, the Cosmological Principle and
the Copernican Principle, which state respectively that the universe is
homogeneous and isotropic, and that we do not occupy a privileged or unusual
region of the universe), but that cosmology must necessarily rely
on untestable assumptions.Ellis
argues, among other things, that the very nature of the project of cosmology
is such that we cannot determine by means of any purely observational test
what the large scale structure of spacetime is.This
in turn means that it is also impossible to test which law of gravitation
holds for the universe as a whole: such a law can only be tested provided
that we know well the very factors Ellis argues are unavailable to us.

The
details of Ellis’s argument are beyond the scope of the present discussion.It
suffices to note that there are two factors that lead to his result.First,
in order to verify any of the main properties of Friedmann-Robertson-Walker
(FRW) universes[2],
one has to assume some or all of the others (no independent check of each
of the properties is possible).Second,
alternative non-FRW cosmological models can always be found which would
account for the observations just as well as any FRW model does.The
clearest case which shows that the characteristics of FRW universes cannot
be tested independently is the case of distortion effects.A
distortion effect is a change in the appearance of a distant object as
compared to what it would look like across a completely flat spacetime,
a change induced by the passage of the light from that object through a
region of spacetime which is distorted (that is, not flat).Distortion
effects can be induced by gravitational lensing by matter, or the distortion
can be caused by large-scale properties of the spacetime itself.In
an FRW universe there would be no distortion effects (the global spacetime
curvature is zero, and the matter distribution perfectly homogeneous and
isotropic).We would therefore
need to confirm that there are no distortion effects in order to confirm
that our universe is actually FRW.But
we cannot check for distortions in the images of distant objects unless
we know what shape they have originally, and obviously we do not have this
information.We cannot, for
example, rule out the possibility that the objects that we call elliptical
galaxies are really spherical objects seen through a distorting spacetime.Even
if we were to treat every source as a point source, finding a perfectly
homogeneous and isotropic distribution of sources across the entire sky
would not prove that there is no distortion effect.This
evidence would be just as consistent with an actually homogeneous and isotropic
source distribution as it would be with any number of inhomogeneous and
anisotropic distributions taken together with suitably selected global
distortion effects.A homogeneous
and isotropic apparent distribution of sources is indeed consistent with
the assumption that the universe is FRW—but observing such a distribution
obviously does not prove that the assumptions of the model are right.

Ellis’s
argument casts into doubt Will’s claim (1993, 310-19) that cosmology has
been a testing ground for gravitation theory since the 1920s.It
is true that various cosmological observations (for example, the Hubble
recession and the cosmic microwave background) have been taken as
confirming that the universe satisfies the Big Bang model, and therefore
the FRW spacetime model (which the Big Bang assumes), and therefore General
Relativity (because the FRW model is a solution to the GR field equations).But
if Ellis’s arguments are correct, this supposed confirmation is illusory
or extremely weak, amounting to no more than showing that GR is consistent
with the available cosmological observations relative to some intuitively
plausible but rather strong and evidentially unsupported assumptions.Relative
to different (and equally unsupported) assumptions, the cosmological evidence
is equally consistent with universe models very different from the FRW
model (for example, ones that are not isotropic or have regions of intrinsic
spacetime curvature).If we
had some way of confirming one set of assumptions over the others, we could
perhaps make some progress toward deciding what the true large scale structure
of the universe is, and this would allow us to confirm a theory of gravitation
at cosmic scales.But if,
as Ellis argues, there is no way to determine empirically whether or not
the universe is in fact homogeneous and isotropic, it is necessarily the
case that there is no way to determine with confidence which spacetime
model fits the universe best.

With
the argument for cosmological scales behind us, let me now turn to the
issue of the evidential basis for applying GR to the scales of galaxies
and clusters.The fact that
GR is not tested at scales larger than a stellar system can be demonstrated
by considering the evidence that is taken to support GR, which I mentioned
earlier.What these tests have
in common is that they involve interactions taking place over relatively
short scales, at most about the size of a stellar system.These
successful tests of General Relativity at short scales are certainly consistent
with GR being the correct gravitational theory at very large distances,
but they do not give us direct evidence that this is indeed the case—the
evidence is also consistent with a very different gravitational action
at large scales.Newton’s
argument to “Universal” Gravitation did not establish empirically that
other stars gravitate but rather used the available evidence of gravitation
among nearby bodies plus some principles of theory choice (Newton’s Rules
of Reasoning) as the foundation for making an inductive extension of the
local law to all bodies.In
the same way, the hypothesis that GR applies at large scales is not supported
empirically by direct evidence.

In
fact, one can construct an argument to suggest that the dynamical evidence
from galaxies and clusters contradicts the hypothesis that GR holds
at those scales.I am referring
here to the evidence of the dynamical dark matter problem, which has to
do with the fact that measurements of the masses of astrophysical systems
such as galaxies and clusters of galaxies taken from their motions are
up to two orders of magnitude greater than the mass estimates taken from
the matter visible in these systems.This
discrepancy can be resolved in one of two ways.Either
we can trust the gravitational law through which the masses are measured
dynamically and postulate the existence of up to 100 times more matter
than is visible in these systems (this matter is called “dark” because
we cannot detect any electromagnetic radiation from it); or we can trust
the visible mass estimates and revise the gravitational law at these scales
so as to be able to recover the motions without needing to introduce unseen
matter.(Note that I am not
here talking about the cosmological dark matter problem, which is another
kettle of fish altogether.)

The
argument to suggest that no gravitational theory can be tested at galactic
and greater scales is based on what I call “the dark matter double bind”,
which goes as follows.Note
that in order to test a gravitational theory, one must show (minimally)
that it correctly predicts the motions of a system of bodies, given some
initial configuration of that system.To
specify the initial configuration, one must specify the distribution of
bodies as well as their masses and velocities.Thus
in order to test GR using the motions of a given spiral galaxy, say, one
needs to know in advance what the mass distribution is.But
the very existence of the dynamical dark matter problem calls into doubt
the assumption that the visible matter is all the matter that exists in
galaxies.In fact, we have
no warranted idea about what the matter distribution might be.Conversely,
if we had reason to think that some particular dynamical law was true of
the galaxy, we could use this dynamical law in concert with observations
of the motions of visible matter to reliably infer the overall mass distribution.But,
as I have suggested above, we have no evidence to confirm that GR (or any
other law) applies to galaxies.Thus,
we cannot obtain a dynamical test of a gravitational theory at galactic
and greater scales unless we assume the matter distribution in advance,
and we cannot empirically determine the matter distribution unless we first
know which dynamical law applies.That’s
the dark matter double bind.

There
might be ways around this conclusion in the future.For
example, we might learn to be able to “see” dark matter, in which case
we could then use the overall distribution of dark and visible matter together
with the motions in a galaxy to determine which gravitational law governs
that system.But in the present
evidential context the existence of the dynamical dark matter discrepancy
for astrophysical systems prevents us from being able to test GR (or any
gravitational theory) at scales greater than those of a stellar system.As
I have suggested, since GR is assumed in almost every part of modern cosmology,
the unavailability of tests of GR means that most cosmological theories
must in fact be only weakly warranted in the present evidential context.This,
I claim, means that whatever evidence we currently have for fine-tuning
is too insecure to license any inferences, whether about a Designer or
the existence of multiple worlds, from that supposed fine-tuning.

Refenences

Ellis,
G.F.R.(1999).“The
Different Nature of Cosmology,” Astronomy and Geophysics, August
1999, 4.20-4.23.

[1]
The gravitational lensing of the light of background objects by foreground
galaxies is a special case I can discuss in the question period if anyone
is interested.(See: Vanderburgh
2001.)

[2]
An FRW universe is a solution to the Einstein field equations for the whole
universe, one that assumes a zero intrinsic curvature and a perfectly homogeneous
and isotropic matter distribution.Among
the interdependent properties of FRW universes identified by Ellis and
homogeneity, isotropy, distortion effects and global curvature.